Math Help - Solving an Exponential equation symbolically using Logarithms

1. Solving an Exponential equation symbolically using Logarithms

I've been working on this problem and I just can't seem to figure it out.

Solve the expression for assuming that all other letters are positive constants.

I just keep running into dead ends where I have t on both sides or both t's on one side.

2. What have you tried so far?

3. Is this ok?

$\displaystyle Pa^t = Vg^t$

$\displaystyle \frac{P}{V} = \frac{g^t}{a^t}$

$\displaystyle \frac{P}{V} = \left(\frac{g}{a}\right)^t$

$\displaystyle t = \log_{\frac{g}{a}}\frac{P}{V}$